specpool {vegan} | R Documentation |
The functions estimate the extrapolated species richness in a species
pool, or the number of unobserved species. Function specpool
is based on incidences in sample sites, and gives a single estimate
for a collection of sample sites (matrix). Function estimateR
is based on abundances (counts) on single sample site.
specpool(x, pool) specpool2vect(X, index = c("Jack.1","Jack.2", "Chao", "Boot","Species")) estimateR(x, ...)
x |
Data frame or matrix with species data. |
pool |
A vector giving a classification for pooling the sites in the species data. If missing, all sites are pooled together. |
X |
A specpool result object. |
index |
The selected index of extrapolated richness. |
... |
Other parameters (not used). |
Many species will always remain unseen or undetected in a collection of sample plots. The function uses some popular ways of estimating the number of these unseen species and adding them to the observed species richness (Palmer 1990, Colwell & Coddington 1994).
The incidence-based estimates in specpool
use the frequencies
of species in a collection of sites.
In the following, S_P is the extrapolated richness in a pool,
S_0 is the observed number of species in the
collection, a1 and a2 are the number of species
occurring only in one or only in two sites in the collection, p_i
is the frequency of species i, and N is the number of
sites in the collection. The variants of extrapolated richness in
specpool
are:
Chao | S_P = S_0 + a1^2/(2*a2) |
First order jackknife | S_P = S_0 + a1*(N-1)/N |
Second order jackknife | S_P = S_0 + a1*(2*n-3)/n - a2*(n-2)^2/n/(n-1) |
Bootstrap | S_P = S_0 + Sum (1-p_i)^N |
The abundance-based estimates in estimateR
use counts (frequencies) of
species in a single site. If called for a matrix or data frame, the
function will give separate estimates for each site. The two
variants of extrapolated richness in estimateR
are Chao
(unbiased variant) and ACE. In the Chao estimate
a_i refers to number of species with abundance i instead
of incidence:
Chao | S_P = S_0 + a1*(a1-1)/(2*(a2+1)) |
ACE | S_P = S_abund + S_rare/C_ace + a1/C_ace * gamma^2 |
where | C_{ace} = 1- a1/N_{rare} |
gamma^2 = max( S_rare/C_ace (sum[i=1..10] i*(i-1)*a_i) / N_rare/(N_rare-1) -1 , 0) |
Here a_i refers to number of species with abundance i and S_rare is the number of rare species, S_abund is the number of abundant species, with an arbitrary threshold of abundance 10 for rare species, and N_rare is the number of individuals in rare species.
Functions estimate the standard errors of the estimates. These only concern the number of added species, and assume that there is no variance in the observed richness. The equations of standard errors are too complicated to be reproduced in this help page, but they can be studied in the R source code of the function. The standard error are based on the following sources: Chao (1987) for the Chao estimate and Smith and van Belle (1984) for the first-order Jackknife and the bootstrap (second-order jackknife is still missing). The variance estimator of S_ace was developed by Bob O'Hara (unpublished).
Function specpool
returns a data frame with entries for
observed richness
and each of the indices for each class in pool
vector. The
utility function specpool2vect
maps the pooled values into
a vector giving the value of selected index
for each original
site. Function estimateR
returns the estimates and their
standard errors for each site.
The functions are based on assumption that there is a species pool: The community is closed so that there is a fixed pool size S_P. Such cases may exist, although I have not seen them yet. All indices are biased for open communities.
See http://viceroy.eeb.uconn.edu/EstimateS for a more complete (and positive) discussion and alternative software for some platforms.
Bob O'Hara (estimateR
) and Jari Oksanen (specpool
).
Chao, A. (1987). Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783–791.
Colwell, R.K. & Coddington, J.A. (1994). Estimating terrestrial biodiversity through extrapolation. Phil. Trans. Roy. Soc. London B 345, 101–118.
Palmer, M.W. (1990). The estimation of species richness by extrapolation. Ecology 71, 1195–1198.
Smith, E.P & van Belle, G. (1984). Nonparametric estimation of species richness. Biometrics 40, 119–129.
data(dune) data(dune.env) attach(dune.env) pool <- specpool(dune, Management) pool op <- par(mfrow=c(1,2)) boxplot(specnumber(dune) ~ Management, col="hotpink", border="cyan3", notch=TRUE) boxplot(specnumber(dune)/specpool2vect(pool) ~ Management, col="hotpink", border="cyan3", notch=TRUE) par(op) data(BCI) estimateR(BCI[1:5,])